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This mathematical monograph details the authors' results on
solutions to problems governing the simultaneous motion of two
incompressible fluids. Featuring a thorough investigation of the
unsteady motion of one fluid in another, researchers will find this
to be a valuable resource when studying non-coercive problems to
which standard techniques cannot be applied. As authorities in the
area, the authors offer valuable insight into this area of
research, which they have helped pioneer. This volume will offer
pathways to further research for those interested in the active
field of free boundary problems in fluid mechanics, and
specifically the two-phase problem for the Navier-Stokes equations.
The authors' main focus is on the evolution of an isolated mass
with and without surface tension on the free interface. Using the
Lagrange and Hanzawa transformations, local well-posedness in the
Hoelder and Sobolev-Slobodeckij on L2 spaces is proven as well.
Global well-posedness for small data is also proven, as is the
well-posedness and stability of the motion of two phase fluid in a
bounded domain. Motion of a Drop in an Incompressible Fluid will
appeal to researchers and graduate students working in the fields
of mathematical hydrodynamics, the analysis of partial differential
equations, and related topics.
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